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- Let <math>S</math> be the set of positive integers <math>N</math> with the property that the last four di ...e numbers are chosen independently and at random with replacement from the set <math>S</math> and labeled <math>a_1,a_2,</math> and <math>a_3</math> in th7 KB (1,257 words) - 17:51, 5 February 2022
- ...y the number of distinct subsets <math>S</math> such of our aforementioned set <math>E_1, E_2, ..., E_n</math> such that the sum of the members in <math>S The only basic ordered pair <math>(E_1, E_2)</math> that offers a nonzero number of legal placemen4 KB (690 words) - 14:32, 6 January 2021
- ...th>(0, 0), (6, 0)</math>, and <math>(0, 5)</math>. Let <math>S</math> be a set of rigid transformations consistsing of rotataions <math>90, 180</math>, an Let there be multiple ordered pairs <math>(n, k)</math> where <math>n</math> and <math>k</math> are posit9 KB (1,450 words) - 18:33, 21 April 2020
- ...math> and <math>b</math> is the ordinal that describes the order type of a set with order type a concatenated with one of order type b. Warning! Ordinal a Every ordinal characterizes the order type of the ordered ordinals less than it. For example, <math>0,1,2,\dotsb,\omega</math> has or5 KB (811 words) - 14:16, 7 June 2020
- ...ordered triple can be identified with a multiset of three elements of the set of <math>2003</math> integers <math>\{17,18,19,\ldots,2019\}</math>, which7 KB (1,186 words) - 15:31, 5 January 2024
- Let <math>S</math> denote the set of all positive integers <math>n</math> that satisfy <math>0 \leq n \leq 10 ...hat he is on <math>(x, y)</math>, he will randomly choose one point in the set <math>\{ (x-1, y-1), (x, y-1), (x+1, y-1) \}</math> to travel to. The proba14 KB (2,267 words) - 12:49, 9 June 2020
- Let <math>S</math> denote the set of all positive integers <math>n</math> that satisfy <math>0 \leq n \leq 10 ...integers (which are ordered accordingly) not including <math>1</math> are ordered based on the placement of the <math>1</math> in the permutation. For instan15 KB (2,388 words) - 13:24, 9 June 2020
- Denote by <math>A</math> the set of all integers <math>a</math> such that <math>1 \le a < p</math>, and both ...value of <math>N</math> over all possible choices of the <math>100</math> ordered pairs.4 KB (614 words) - 13:47, 22 November 2023
- ...th>, we can first choose two different numbers <math>a > b</math> from the set <math>\{0,1,2,\ldots,10\}</math> in <math>\binom{11}{2}=55</math> ways. Thi As indicated by the X-marks, the ordered pairs <math>(a,b)=(10,0),(10,1),(10,2),(10,3),(10,4)</math> generate <math>7 KB (1,174 words) - 08:21, 13 May 2023
- ...uence<cmath>3, 4, 5, a, b, 30, 40, 50</cmath>is strictly increasing and no set of four (not necessarily consecutive) terms forms an arithmetic progression8 KB (1,205 words) - 22:55, 26 March 2023
- For any finite set <math>X</math>, let <math>| X |</math> denote the number of elements in <ma where the sum is taken over all ordered pairs <math>(A, B)</math> such that <math>A</math> and <math>B</math> are s9 KB (1,471 words) - 16:41, 1 February 2024
- Let <math>\mathbb Q_{>0}</math> be the set of all positive rational numbers. Let <math>f:\mathbb Q_{>0}\to\mathbb R</m ...>M</math> be the number of beautiful labelings, and let N be the number of ordered pairs <math>(x, y)</math> of positive integers such that <math>x + y \le n<4 KB (696 words) - 05:43, 17 February 2021
- ...</math> and two sides with lengths <math>4</math> and <math>10</math>. The set of all <math>s</math> for which <math>\tau(s)</math> is nonempty, but all t .../math> denote the number of elements in <math>S</math>. Find the number of ordered pairs <math>(A,B)</math> such that <math>A</math> and <math>B</math> are (n8 KB (1,429 words) - 14:31, 26 February 2024
- Over all ordered triples of positive integers <math>(a,b,c)</math> for which <math>a+b+c^2=a ...exists an integer <math>n\ge2020</math> such that when the elements of the set <math>\{1,2,\ldots,n\}</math> are sorted lexicographically from least to gr8 KB (1,298 words) - 18:32, 7 January 2021
- ...pairs <math>(t,b')</math> have one-to-one correspondence, we consider the ordered pairs <math>(t,b')</math> instead. The requirements become <math>t\equiv8-b Consider the set of all <math>2^{8+6}=2^{14}</math> possible choirs that can be formed. For8 KB (1,183 words) - 00:36, 27 May 2024
- ...</math> by <math>2</math> square centered at <math>(3x, 3y)</math> for all ordered pairs of integers <math>(x, y).</math> ...th>(0, 0)</math>. (minus the teleportations) Since counting the complement set is easier, we'll count the number of <math>4</math>-step paths such that Fr17 KB (2,801 words) - 07:29, 4 November 2022
- Find the number of ordered positive integer triplets <math>(a,b,c)</math> such that <math>a</math> eve ...ith imaginary part greater than <math>0</math>. Let <math>T</math> be the set of all <math>9</math>th primitive roots of unity with imaginary part greate7 KB (1,149 words) - 17:16, 15 December 2020
- ...y)</math> which both <math>x</math> and <math>y</math> are elements in the set <math>\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15\}</math>, <math>x</math> and < What can be a description of the set of solutions for this: <math>x^{2}+y^{2}=|2x+|2y||</math>?15 KB (2,366 words) - 17:45, 19 September 2021
- ...> such that <math>m</math> and <math>n</math> are positive integers in the set <math>\{1, 2, ..., 30\}</math> and the greatest common divisor of <math>2^m To count the ordered pairs <math>(m,n),</math> we perform casework on the number of factors of <7 KB (1,212 words) - 15:54, 15 April 2024
- ...i\sqrt{3}}{2},</math> where <math>i = \sqrt{-1}.</math> Find the number of ordered pairs <math>(r,s)</math> of positive integers not exceeding <math>100</math ...e sequence <cmath>3,4,5,a,b,30,40,50</cmath> is strictly increasing and no set of four (not necessarily consecutive) terms forms an arithmetic progression9 KB (1,520 words) - 19:06, 2 January 2023
